Ok so I might be doing something silly but I just don't understand what is going on here. So the integral:(adsbygoogle = window.adsbygoogle || []).push({});

i = ∫ sin x (cos x)^3 dx

First I say u = cos x. So du = - sin x dx.

So now I have i = ∫ - u^3 du. Which gives: i = -(1/4)u^4 or -(1/4)(cos x)^4. Easy.

But if I say u = sin x instead, this is what happens:

So du = cos x dx. And I say i = ∫ sin x (cos x)^2 cos x dx.

So I have i = ∫ u(1 - u^2) du or i = ∫ (u - u^3) du. WHAT.

Why am I getting two different answers?? Which one is right and why?

Thanks!

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# Integration by substitution for sin/cos products

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